Title | Identifying Sources of Thermoacoustic Vibrations in Industrial Furnaces and Boilers |
Creator | Flynn, T.J. |
Contributor | Fuller, T.A., Rufener, S., Finney, C.E.A., Daw, C.S. |
Date | 2018-09-18 |
Description | Paper from the AFRC 2018 conference titled Identifying Sources of Thermoacoustic Vibrations in Industrial Furnaces and Boilers |
Abstract | Industrial gas-fired boilers, furnaces and heaters occasionally suffer low-frequency vibrations generated by dynamic feedback between the burner (or burners) and acoustic modes in adjacent cavities in the main combustion chamber or ductwork. Feedback occurs when pressure pulses associated with acoustic resonances propagate to the burner so that they are in phase with combustion rate fluctuations. When the combustion and acoustic fluctuations become sufficiently phase-synchronized, normal sources of dissipation are insufficient to damp the combined pressure waves, and they can become sufficiently amplified to reduce thermal efficiency, increase emissions, and even cause structural damage. In the literature, such oscillations are referred to as thermoacoustic oscillations or ‘rumble', and their basic physics have been the subject of numerous investigations for well over a century. Although it occurs relatively infrequently, rumble poses a significant challenge because it is difficult to predict, diagnose, and resolve. The underlying relationships involved are sufficiently complex that it is possible for two apparently identical boilers or furnaces to exhibit completely different rumble tendencies. In this study, we review common sources of rumble and how nonlinear signal analyses, such as bivariate mutual information and transfer entropy, can be used to locate both its sources and impact in boilers, furnaces and heaters. |
Type | Event |
Format | application/pdf |
Rights | No copyright issues exist |
OCR Text | Show Presented to: AFRC 2018 Industrial Combustion Symposium September 17-20, 2018, Salt Lake City, Utah, USA IDENTIFYING SOURCES OF THERMOACOUSTIC VIBRATIONS (RUMBLE) IN INDUSTRIAL FURNACES AND BOILERS † Thomas J. Flynn, Timothy A. Fuller, and Suzana Rufener The Babcock & Wilcox Company Barberton, OH USA Charles E.A. Finney and C. Stuart Daw Oak Ridge National Laboratory Oak Ridge, TN USA ABSTRACT Industrial gas-fired boilers, furnaces and heaters occasionally suffer low-frequency vibrations generated by dynamic feedback between the burner (or burners) and acoustic modes in adjacent cavities in the main combustion chamber or ductwork. Feedback occurs when pressure pulses associated with acoustic resonances propagate to the burner so that they are in phase with combustion rate fluctuations. When the combustion and acoustic fluctuations become sufficiently phase-synchronized, normal sources of dissipation are insufficient to damp the combined pressure waves, and they can become sufficiently amplified to reduce thermal efficiency, increase emissions, and even cause structural damage. In the literature, such oscillations are referred to as thermoacoustic oscillations or ‘rumble', and their basic physics have been the subject of numerous investigations for well over a century. Although it occurs relatively infrequently, rumble poses a significant challenge because it is difficult to predict, diagnose, and resolve. The underlying relationships involved are sufficiently complex that it is possible for two apparently identical boilers or furnaces to exhibit completely different rumble tendencies. In this study, we review common sources of rumble and how nonlinear signal analyses, such as bivariate mutual information and transfer entropy, can be used to locate both its sources and impact in boilers, furnaces and heaters. Objectives In a previous paper [Flynn (2017)], the current knowledge about the causes of thermoacoustic vibrations in industrial natural-gas-fired furnaces and boilers was summarized, and opportunities for enhancing diagnosis and remediation were identified. In this study, we review the most pertinent references, describe the issue of thermoacousticinduced vibrations in more detail for gas-fired boilers, and extend the application of some of the previously suggested nonlinear analysis techniques, such as bivariate mutual information and transfer entropy. Limitations and Scope The experimental data included in this study was generated without the benefit of controlled experiments on industrial-scale units. Instead, field measurements were collected from a commercial boiler to illustrate an actual case of industrial relevance, its quantitative characteristics, and how it compared with expected patterns. Future experimental field tests are being planned for this and other units that will provide additional data to improve basic understanding of the problem and support improved designs and/or operating strategies. We specifically do not address the problem of flow-induced vibration here, which can also occur in industrial furnaces and boilers. INTRODUCTION Note: Significant components of the introductory and methodology descriptive text herein are included verbatim from our paper from last year's AFRC meeting [Flynn, 2017]. We choose this approach of verbatim inclusion over reference to make this paper selfcontained in its narrative, in case of limited availability of the cited paper. Compared with last year's paper, the present paper expands focus on application, adds analytical methodology, with different results and conclusions. † 1 Babcock & Wilcox The source of thermoacoustic vibrations (rumble) in industrial furnaces and boilers is distinct from flow-induced vibration and is more closely related to the ‘singing flame' phenomenon in heated tubes, which has been studied in various forms since the 18 century [Richardson (1922)]. Thermoacoustic vibrations always require the presence of two key features: 1) a large temperature gradient, and 2) a gas-filled cavity capable of supporting Helmholtz resonances [Chanaud (1994), Seebold (2005), Balasubramanian & Sujith (2008), Eisinger & Sullivan (2002, 2008)]. The underlying physics of this phenomenon was originally explained by Rayleigh [(1878)], who noted that the key requirement for sustained vibrations is met when the rate of change in pressure in the vicinity of a flame or hot surface becomes directly correlated with the rate of heat input (either via reaction or transfer from a hot surface). More recently, Nicoud and Poinsot [(2005)] suggested that the requirement for vibrations in combustion systems is also met when the rate of temperature rise becomes directly correlated with the reaction rate. In either case, the key requirement is to have synchronized phasing between the rate of heat input and the rate of gas compression/expansion. In some of the most definitive studies to date, Eisinger and Sullivan [(2002, 2008)] showed that large temperature differentials between the cold burner inlet air and the hot combustion gases can lead to such phase synchronization in industrial-scale furnaces and boilers. Other key factors are the lengths of the burner cavity and the hot gas zones, which provide the necessary spatial domains and boundary conditions for the development of standing acoustic (pressure) waves that can be excited by input heat energy. Two common standing-wave patterns that originate in the burner are referred to as either the Rijke or Sondhauss modes, which are named after their original experimental discoverers [Balasubramanian (2008), Rott (1983), Eisinger & Sullivan (2002, 2008)]. Synchronization occurs when there is constructive interference between these standing waves and downstream resonances in the post-burner hot zone. When this happens, thermal energy from combustion is converted into acoustic energy. Under normal operation, furnaces and boilers typically have large temperature differentials between the hotter product gases and the cooler reactant air, thus there is a large thermal energy source to sustain these oscillations once they begin. Eisinger and Sullivan presented a map that delineates operating and design regions where synchronization is likely in furnaces and boilers. As shown in Figure 1, two dimensionless parameters, representing the key geometric and temperature factors, are used to determine whether any given system falls into the stable (non-vibrating) or unstable (vibrating) region. Typical load isotherms are plotted relative to these regions in Figure 1 for a wide range of burner and furnace system geometries. As can be seen in the figure, thermoacoustic instability tends to increase with load for many different geometric configurations. th Figure 1. Thermoacoustic vibration stability curve [after Eisinger and Sullivan (2008)] with typical load isotherms. Often the key geometric factors responsible for thermoacoustic vibrations in a specific unit are difficult to identify because of the complex interaction of firebox and duct design characteristics that can be involved in the standing wave patterns. Rumble also often appears during specific types of operating transients or load states (typically at intermediate or part load states), so it may not always be observed until after a unit has been initially constructed and tested. This intermittent nature can also make rumble difficult to characterize and correlate with operational events. It is not uncommon for two "identical" boilers to be just different enough such that one unit will exhibit vibration while the other will not at apparently identical operating conditions. Much work has been done to characterize thermoacoustic vibration in combustion systems, but slight variations in geometry and structural rigidity can still allow unanticipated vibration to occur. Babcock & Wilcox 2 Fuel variations can also be involved in the appearance of rumble. Many industrial boilers have a single burner that is designed to fire a variety of fuels, including natural gas, #6 or #2 oil, syngas, biogas or waste gas depending on which fuel is most readily available at the lowest cost. Although natural gas is currently the lowest cost fuel, its composition can vary significantly depending on the source, and non-price driven supply issues can also result in fueling shifts. Whatever the cause, the specific combustion properties of different fuels can have a significant impact on combustion and heat release and thus promote or suppress the onset of rumble. When rumble occurs, it is sometimes possible to make operational adjustments (e.g., changing burner settings or avoiding certain firing rates) that directly improve the burner or acoustic parameters themselves or that suppress the interactive feedback; in some instances, disrupting standing acoustic waves is a strategy [Seebold (2005)]. In many cases, however, operating adjustments are not sufficient to solve the problem, and it may only be possible to take measures that reduce the resulting vibrational damage (e.g., adding mechanical stiffeners to vibrating components) rather than removing the original source of the problem. Ideally, if our understanding of the rumble phenomenon is sufficient, it should be preferable and less costly to remove the underlying causes by more effectively avoiding certain design features and/or developing and implementing more effective active control measures that suppress feedback. For the latter, it might even be possible to implement such controls post factum in existing units. In the following sections, we summarize the information currently available in the literature about both of these possible approaches. We also believe it is important to consider methods that might be used for diagnosing rumble in individual cases to better identify root causes and thereby reduce the cost and time associated with resolving the problem. We illustrate possible approaches for the latter with example field data collected from a boiler experiencing rumble. BACKGROUND Thermoacoustic vibrations can occur in a wide range of combustion systems operating in both fuel-lean, or fuel-rich conditions, as long as the conditions necessary for constructive interference between heat input and acoustics are met. Fuel-lean conditions are often chosen to minimize NO emissions in combustion turbines, and these tend to shift the main heat-release zone upstream into the burner throat while also reducing the temperature of the post-burner gases. Both of these changes affect the relative locations of the heat release and acoustic (pressure) waves. Excessively lean operation can also lead to flame lifting, which leads to transient shifts in the flame location and length that cause jumps back and forth across the stability boundary in Figure 1 (e.g., see Daw (2002)). Fuel-rich conditions coupled with air staging are often chosen for industrial boilers to minimize NO emissions, but these can also lead to longer and cooler flames, shifts in sound speed, and corresponding shifts in acoustic wave lengths. x x Studies of Thermoacoustic-Induced Vibrations Rodriquez-Martinez et al. (2006) studied instabilities in a partially premixed swirl burner and furnace test rig. The testing also included the effect of the inlet air duct geometry on the instabilities. Low-frequency (30-100 Hz) instabilities were characterized. Unstable pressure amplitudes greater than 5% of the mean pressure were observed. They concluded that the instabilities result from excitation of the longitudinal modes of the air supply ducting which formed the dominant acoustic geometry of their test rig. They note that their test rig exhibits similar behavior to that observed in pulse combustors, dump combustors and gas turbines where the flame dynamics are strongly coupled to upstream modulations in air flow. This could also be true for industrial natural-gas furnaces where furnace dynamics can be influenced by the dynamics of the forced-draft fan, control dampers or duct geometry. The length of the inlet duct had a significant impact on the pressure and velocity oscillation modes in the combustor. Generally, the velocity lagged the pressure by one-quarter cycle which they note is indicative of standing waves. Acharya et al. (2013) analyzed premixed swirl flames subject to helical flow disturbances. The study was motivated by combustion instabilities and combustion noise. Combustion instabilities occur when unsteady heat release couples with one or more of the combustor's acoustic modes. High-amplitude pressure and velocity oscillations can occur. The analysis shows that helical modes can influence the flame "wrinkling" amplitude and heat-release fluctuations differently. The instability parameters exhibit variations in sensitivity to swirl number and other flame parameters. This paper provides a good theoretical analysis of combustion instability. Sams and Jordan (1996, 1997) investigated natural gas burners for firetube indirect heaters. They show with test data that when the burner nozzle velocity is sufficiently greater than the firetube velocity, the low-frequency rumble decreases. Field data was used to construct relationships between the burner noise level and the gas volume expansion ratio, burner air-to-fuel ratio, mixture flow rate, natural gas orifice velocity, burner area, and the number of burners. They developed a correlation to predict burner noise. Burner rumble will occur when the velocity head ratio of the burner nozzle to combustion chamber is outside the range of 7 to 50. 3 Babcock & Wilcox Iordache and Catalina (2013) performed sound level measurements on two small (770 kW) commercial building heating boilers over the entire boiler operating cycle. Somewhat unexpectedly they found that the highest sound levels were recorded during the ventilation period of the boiler cycle before gas injection rather than at the maximum thermal load period. This indicates that air flow dynamics can be a plausible source of vibration and noise. Kodis, Webster and Dirks (2002) reported an instance where a dirty air heater was the cause for furnace rumble. Goldring (2007) used a computational fluid dynamics model to illustrate flame detachment as a function of combustion parameters. The modeling was used to show that the planned burner modifications, which included new staged flame stabilizers, low-NO gas lances and low-NO atomizers would produce stable flames over the load range and with a wide range of flue gas recirculation (FGR). Combustion instabilities in industrial furnaces could arise in low-NO burners as the combustion limit is approached due to fuel-rich conditions. Eckstein et al (2004) studied the role of entropy waves in low-frequency oscillations for a diffusion burner. x x x Potential Corrective Measures There are two possible approaches to mitigate vibration in industrial boilers or combustion turbines. The equipment can be mechanically altered to reduce or eliminate the vibration. Adaptive or passive control techniques can be used to alter the combustion process to eliminate or reduce vibration. Eisinger and Sullivan (2002, 2008) suggest simple changes to the inlet configuration of the burner to address furnace rumble by slightly altering the operation of the burner relative to the stability line and moving the operation into the novibration region. Berkau et al. (1990) use natural gas co-firing to stabilize a deeply staged, low-NO coal burner. By introducing natural gas into the primary air line with the coal, the combustion instability is reduced over the load range and better attachment is achieved. By eliminating the fluctuations due to ignition and extinction at the burner front in a deeply staged burner, furnace rumble is eliminated. Lifshits et al. (1994, 1995) eliminate combustion instability in natural-gas industrial burners by more uniformly distributing the natural gas and primary air. This is not a premixed burner. They distribute the gas through small holes along radial slots in the primary zone. Since the gas and air are mixed radially, local oscillations of the flame front occur at different frequencies and therefore do not synchronize, which dampens vibration and resonance problems. This approach was specifically invented to address furnace rumble due to staging the combustion in low-NO burners to reach ultra-low NO emissions. Han (2008) used a tunable Helmholtz resonator to dampen oscillations. Both the cavity volume (piston) and throat plate (exchangeable) could be adjusted to alter the resonant frequency. This work provides a nice presentation of calculations of Helmholtz resonance frequency. The Helmholtz resonator was affixed to the side of a cylindrical duct at the end of which was a horn that could be tuned to a range of frequencies. This is an example of adaptive tuning. Candel (1992) employs active control in a pulse combustor. It is shown that in the presence of pressure waves, large-scale motions drive the instability. The paper describes the processes that drive the flame dynamics such as hydrodynamic instability, vortex roll-up, vortex interactions, front and reacting stream pulsations, periodic extinctions and reïgnitions, and self-acceleration. The paper reviews the basic principles and the initial demonstrations of active instability control of pulse combustors. The application of adaptive control methods is discussed in more detail. x x x RESULTS FROM A RECENT B&W BOILER CASE STUDY Recently, Babcock &Wilcox (B&W) personnel have observed thermoacoustic vibrations first-hand on several industrial boilers. To better understand the problem in a specific case, field measurements were collected from a small natural gas-fired industrial boiler that was experiencing vibrations of an apparently thermoacoustic origin. Multiple types of instrumentation were used to measure the vibrations including: microphones; high temperature accelerometers; IEPE (Integrated Electronics, PiezoElectric) accelerometers; and dynamic pressure transducers. These sensors were installed throughout the flow path as shown in the plan view in Figure 2, beginning at the FD fan discharge duct (air inlet duct), then the furnace, followed by the generating bank and the boiler outlet / economizer. Babcock & Wilcox 4 Figure 2. Simplified boiler arrangement and layout of microphones. During the measurements, the boiler was operated in the load range where significant vibrations were known to occur. Performance parameters of the boiler, such as air mass flowrate and density, were adjusted to determine what impact each of the parameters would have on the boiler pulsation. The only adjustment that appeared to impact the boiler pulsation was increasing or decreasing the firing rate beyond the pulsation range. The characteristic frequency spectrum measured during the furnace pulsation appeared to be a low-frequency, highamplitude peak with a sawtooth shape, indicating nonlinearity in the signal. While the amplitude was significantly reduced outside of the pulsation range, the peak frequency remained the same regardless of firing rate. The field data were further analyzed to determine the source of the thermoacoustic vibration, and to determine which parameters impact the vibration. The signals were compared and studied to identify whether geometric characteristics or combustion characteristics, or a combination of both, have the most impact on the vibration. Of specific interest is the development of a design specification that would optimize the design of industrial boilers and reduce the potential for thermoacoustic vibration in the future. ANALYSIS OF THE B&W FIELD DATA As a preliminary step in analyzing the B&W field case data, we analyzed the basic time-series characteristics of the microphone time series to resolve the general trends they revealed about the vibrations. These analyses included: • Signal oscillograms - Depiction of the qualitative patterns in the raw signals • Power spectral density functions - Measure of dominant frequency content • Temporal irreversibility (T ) functions - Measure of temporal asymmetry in signal oscillations • Cross-correlation functions - Measure of linear correlation over finite timescales Future analyses are planned that will include more sophisticated information-theoretic functions such as transfer entropy to quantify the degree and sense of information flows between measurement locations. 3 ANALYTICAL RESULTS FOR THE FIELD DATA Signal oscillograms Figure 3 illustrates the temporal patterns detected by the four acoustic transducers (microphones) at the locations depicted in Figure 2 for a test in which the boiler unit transitioned from rumble to normal operation and back to rumble after a ramped-up load change. We examine three 60-s segments of the test, as denoted on the figure, where the burner firing rate 5 Babcock & Wilcox was nominally the same, with the only difference being the spontaneous transition out of and back into rumble. Looking at the entire timespan in the figure, the signal envelopes are quite variable, representing overall sound-intensity changes in the boiler unit. Additionally, the long-term drift in the envelope, as seen from 0 to 120 s, is visible and represents a long-term controlled change in firing rate. At about 120 s onward, the firing rate is nominally the same, and changes largely reflect uncontrolled, spontaneous system responses. Figure 3. Complete time records for the microphone signals, from top to bottom: firebox (2); FD fan area (4); inlet duct (3); generating bank (1). All the time series are plotted on the same scale. 60-s segments used in later analysis are marked by the red boxes and lettered for reference. Microphone numbers are from Figure 2. On small timescales, however, distinct differences in the acoustic signal at each location are noted, as depicted in Figure 4. In the rumble condition segments, a dominant oscillation of about 10 cycles per second is observed, with higher-frequency content superimposed to varying degrees, depending on measurement location. The signals have very similar characteristics in both rumble segments, even after having spent several minutes in "normal" operation in the interim. The normal-condition signals do contain a discernible large-scale oscillation frequency of about 10 cycles per second, but the higher-frequency signal content is of equal or greater magnitude. The boiler vibrations, as measured by the acoustic sensors, do appear to resonate at a natural system frequency. Babcock & Wilcox 6 Figure 4. Time-series segments for the microphones at three conditions: rumble (A), normal (B), rumble (C). All segments encompass 1 s of time on the abscissa and are scaled to the segment signal range on the ordinate. Frequency content These observations regarding the relative frequency content of the signals is reflected in the power spectral density (PSD) functions, as shown in Figure 5. In this figure, the plots' axes are shown on the same scale, with log of power on the ordinate and frequency ranging from 0-100 Hz on the abscissa, with the 10 Hz frequency highlighted. For all signals, there is a distinct dominance of the 10 Hz oscillation. In the rumble cases, sharp harmonics of 10 Hz are pronounced, suggestive of the coherence in the signals at the primary harmonic. In the normal case, the harmonics are not significant, but other broadband frequency content, not necessarily at multiples of 10 Hz, is present within 1-2 decades of the 10 Hz content, 10 7 Babcock & Wilcox suggesting a more complex signal dominated by higher-dimensional causes than observed in the resonance seen in the rumble condition. Figure 5. Power spectral density functions for the microphones at three conditions: rumble (A), normal (B), rumble (C). All spectra plotted on same log scale, from 0-100 Hz, with 10 Hz highlighted. 10 A question remains regarding the physical cause behind the 10 Hz natural frequency. This is significant because it does not seem to correspond to the Rijke or Sondhauss modes suggested by Eisinger and Sullivan (2002, 2008) as being the primary modes expected to be associated with thermoacoustic vibrations. In the cases they studied, for similar boiler dimensions, the expected frequencies were typically in the range of 30-50 Hz. Thus, there appears to be some other factor involved that is not accounted for by previous work in the literature. One possible explanation for the 10 Hz oscillation is that there could be some type of constructive interference between the forced-draft air fan and the furnace cavity. The fan has a maximum speed of around 1800 RPM, or 30 revolutions per second, and this speed varies depending on the firing rate. In the conditions measured here, the frequency range caused by the blade passages is thought to be around 180 Hz. To some extent, the fan oscillation frequency, coupled to the overall volume of the supply system and firebox, could explain the observations, and we are investigating to within the limits of available design and operating data to verify this assumption. Another possibility is that the expected relationship between the pre- and post-burner resonance zones (i.e., between the air inlet and furnace cavities) that leads to the dominant frequency oscillations may not apply in this particular case. More specifically, it may be that the Rijke and Sondhauss modes are not dominant here, but instead there is another set of acoustic modes that are interacting with the heat release from the burner to drive a lower frequency resonance. This might occur if the characteristic wave length in the air inlet is actually different than suggested by Eisinger and Sullivan, resulting in the creation of a lower-frequency beating between the air inlet and furnace zones. As with the fan coupling, we are also investigating these other modes as possible root causes. Time irreversibility Babcock & Wilcox 8 One of the more sophisticated analytical tools we are using to help understand the 10 Hz oscillations is time irreversibility. As is slightly visible in Figure 4, the large-amplitude acoustic waveforms were sawtooth shaped. For instance, for the fan-area transducer (microphone 4), the waveform has a slow rise to the cycle maximum and then a rapid fall to the cycle minimum; the opposite is seen for the air-duct transducer (microphone 3). Time asymmetry is important because Gaussian sources, or static transforms thereof, are temporally reversible, meaning that there is a statistical difference in time-sensitive metrics depending on whether the signal is examined in the forward or reverse sense. A metric capturing this difference, the T function, is displayed in Figure 6. Each plot ordinate contains the same scale - the T metric is normalized - and the abscissa displays timescales from 0-0.2 s, much like with correlation functions. This time range captures roughly two cycles of the fundamental oscillation of the microphone signals. We note that opposite trending patterns occur in microphones 3 and 4. Additionally, the normal, non-rumble mode T metrics are close to 0, suggesting a different cause than in the rumble conditions. Irreversibility is a hallmark of nonlinearity, and in many combustion systems, flame-oscillations are known to be temporally asymmetric. Thus, the observation of pronounced irreversibility suggests that the flame is a key component of the vibrations, and thus the root cause is thermoacoustic vs. flow-based resonance. 3 3 3 Figure 6. T (irreversibility) functions for the microphones at three conditions: rumble (A), normal (B), rumble (C). All functions plotted on same scale, from 0-0.2 s lag, with T =0 highlighted. 3 3 Correlation analysis In thermoacoustic oscillations, pressure/sound waves are expected to propagate outward from the flame. In the field tests, we did not have the opportunity to measure this directly. However, with spatially separated microphone measurements recorded simultaneously, the cross-correlation in the signals can provide some insight. In the analysis below, we will use the air inlet duct microphone as the reference signal location, as it was closest to the base of the flame. 9 Babcock & Wilcox We use two metrics to compare the temporal correlation between the FD fan, the firebox, and the generating bank signals referenced to the inlet duct signal. The first metric is the cross-correlation function, which quantifies the linear correlation, or covariance, of two signals over a range of timescales. Cross-correlation is frequently employed in flow systems to measure timescales for spatial propagation of waves or flows. The second metric is the bivariate mutual information function, which quantifies the cross-mutual information of two signals over a range of timescales. As such, the bivariate mutual information may be thought of as a generic, not necessarily linear, measure of correlation. In both types of correlation, comparison of signal correlation is typically referenced as signal Y with respect to (wrt) signal X. Positive correlation of Y wrt X means that Y lags or follows X at the given time delay. The mutual information function always has positive values, whereas cross-correlation values may have negative values, for anticorrelation. In our implementation, crosscorrelation is normalized by the covariance of X and Y, so its values range from -1 to +1; the bivariate mutual information is positive, in units of bits. The cross-correlation functions for unique pairs of microphone signals is portrayed in Figure 7. A few general features of the cross-correlation functions may be noted. First, during rumble, there is stronger correlation compared with non-rumble between pairs of microphone signals, owing to the stronger coherence of each signal (even though this difference is not as apparent as with the T ). Second, certain relationships are apparent in the locations of the correlation peaks. For instance, signal 1 lags signal 2 (top-most row), meaning the oscillation waveform happens in signal 2 before 1 (or at the firebox back wall before the generating bank), and signals 3 (inlet duct) and 4 (fan area) precede 2 (firebox back wall), suggesting a propagation of information from the fan or burner area downstream. However, because of the long-term cyclic persistence observed in the correlation functions, it is difficult to produce an exact mapping of information (pressure) propagation. 3 Figure 7. Cross-correlation functions for the microphones at three conditions: rumble (A), normal (B), rumble (C). All functions plotted on same scale, from -0.1-+0.1 s lag, with 0-axes highlighted. Positive correlation of Y wrt X means that Y lags or follows X at the given time delay. Babcock & Wilcox 10 A comparison of the mutual information with cross-correlation for select microphone signal pairs is seen in Figure 8. Many of the significant timescales match between the two correlation metrics (remembering that the anti-correlation troughs in cross-correlation appear as peaks in the mutual information, which is always > 0). Figure 8. Comparison of cross-correlation and mutual information for select microphone signal pairs. 11 Babcock & Wilcox In interpreting these timescales, we first must understand the conditions in the gas flow path, especially focusing on the speed of sound. Correlation timescales must be longer than the sound travel time between the pair of sensors, or else they are spurious. Based on process conditions and physical distances between sensors, estimates of relative conditions are shown in Table 1. The speed of sound ranged from ~355 to ~775 m/s depending on the chamber - the hot gases in the firebox have the highest speed of sound, with the generating bank the next highest, and the inlet duct and FD fan area the lowest. In calculating the speed of sound in a chamber, the gas composition and temperature were assumed to be homogeneous, and travel times were summed between chambers with different compositions. Table 1. Correlation timescales between microphone pairs. Microphones Generating Bank wrt Firebox Generating Bank wrt Inlet Duct Firebox wrt Inlet Duct FD Fan wrt Inlet Duct Distance [m] 4 16 13 2.8 Sound time [ms] Correlation time [ms] 6 20 27 55 21 60 8 18 Sense GB lags Firebox GB lags Inlet Duct Firebox lags Inlet Duct Inlet Duct lags Fan The correlation times generally confirm a propagation of information from the inlet duct area, specifically near the FD fan, downstream. The thermoacoustic instability seems to interact with and amplify the ~10 Hz natural frequency during rumble. Work is ongoing to define the natural frequency as well as identify means to disrupt its coherence. In future work, we plan to continue analysis with general, information-theoretic measures such transfer entropy to refine the sense of the information flows between sensors. The first pass of analysis suggests that information flows from the base of the flame area outward, which is consistent with a thermoacoustic mechanism, during rumble, given the strong time irreversibility. Further, there is no dominant flow-induced vibration effect propagating upstream from the generating bank. CONCLUSIONS In a limited study of boiler field measurements, we have observed pronounced resonant oscillations in microphone signals collected at several points around a single-burner gas-fired unit. The dominant frequency of these oscillations suggests that some process other than the fundamental thermoacoustic modes predicted by the Rijke and Sondhauss models is the primary root cause of the vibrations. Nevertheless, the presence of time asymmetry strongly implies that driving energy for the vibrations comes from the burner rather than flow instabilities (i.e., the vibrations are thermoacoustic rather than flow induced). To a limited extent, we are able to detect correlation patterns between measurement points that indicate how the main furnace cavity and burner are spatially coupled. Future work will focus on verifying these results with more extensive data from other sensors as well as employing more sophisticated information-theoretic correlation measures to pinpoint the spatial sources of oscillations. Additionally, more rigorous analysis of the geometric and thermal driving sources can reconcile the observed vibrational frequency with analytical solutions. This will enable more selective design changes or operational controls to eliminate rumble in operating industrial furnaces and boilers. ABBREVIATIONS CFD FGR IEPE NASA PSD T Computational Fluid Dynamics Flue Gas Recirculation Integrated Electronics, PiezoElectric National Aeronautics and Space Administration Power Spectral Density Temporal Irreversibility Function 3 SYMBOLS L = Characteristic acoustic length of furnace cavity [m] l = Characteristic acoustic length of burner air inlet [m] T = Furnace (post-burner) temperature [K] T = Burner air inlet temperature [K] ξ = (L-l )/l = Characteristic geometric parameter for Rijke and Sondhauss resonance modes [-] 1 1 2 1 1 Babcock & Wilcox 12 REFERENCES Acharya V.S., Shin D. -H., Lieuwen T. (2013). Premixed flames excited by helical disturbances: Flame wrinkling and heat release oscillations. Journal of Propulsion and Power 29(6): 1282-1291. doi:10.2514/1.B34883. Balasubramanian K., Sujith R.I. (2008). Thermoacoustic instability in a Rijke tube: Non-normality and nolinearity. Physics of Fluids 20: 044103. doi:10.1063/1.2895634. 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Ultra-low NO burners can get even better: tougher emission rules are forcing development of even more effective utlra low NO burners. Power Engineering, November 2008, 144-154. x x Wood S.C. (1994). Select the right NO control technology. Chemical Engineering Progress, January 1994, 32-38. x Copyright © 2018 The Babcock & Wilcox Company. All rights reserved. No part of this work may be published, translated or reproduced in any form or by any means, or incorporated into any information retrieval system, without the written permission of the copyright holder. Permission requests should be addressed to Marketing Communications by contacting us from our website at www.babcock.com. ACKNOWLEDGEMENT Portions of this work were supported by the U.S. Department of Energy's (DOE) Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office's (AMO), Combined Heat and Power Research Program, and performed at Oak Ridge National Laboratory (ORNL) by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725. The authors thank Bob Gemmer of the AMO for his support. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). 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Reference URL | https://collections.lib.utah.edu/ark:/87278/s6k97jks |